Mathematical Patterns

Question 1

Recurring geometric forms, or numbers that are sequence in such a way that they follow certain rules.

Answer 1

Mathematical patterns

Question 2

Common mathematical patterns that we encounter daily

Answer 2

Number patterns, the logic patterns and the geometric patterns

Question 3

Number patterns

Answer 3

Arithmetic sequence
Geometric sequence
Fibonacci sequence

Question 4

Set of numbers arranged in some orders.

Answer 4

Sequences

Question 5

Each of the numbers of a sequence is called _____________.

Answer 5

Term of the sequence

Question 6

The first term is symbolized by

Answer 6

a sub 1

Question 7

Second term is symbolized by

Answer 7

a sub 2

Question 8

The nth term is symbolized by

Answer 8

a sub n

Question 9

A sequence of values follows a pattern of adding a fixed amount (always the same) from one term to the next.

Answer 9

Arithmetic sequence

Question 10

The fixed amount in arithmetic sequence is called __________.

Answer 10

Common difference

Question 11

How to find the common difference?

Answer 11

Subtract the first term from the second term.

Question 12

Formula in finding the common difference

Answer 12

d=a sub 2 - a sub 1

Question 13

A sequence of values follows a pattern of multiplying a fixed amount from one term to the next.

Answer 13

Geometric sequence

Question 14

The fixed amount that is used to multiply one term to the next.

Answer 14

Common ratio

Question 15

Geometric sequence formula

Answer 15

a sub n = r (a sub n - 1)

Question 16

Common ratio formula

Answer 16

r = a sub n/ a sub n - 1

Question 17

How to find the common ratio

Answer 17

Common ratio is found by dividing any term by its previous term.

Question 18

This can be used to find any term in geometric sequence.

Answer 18

Common ratio formula

Question 19

A set of numbers developed by Leonardo Fibonacci.

Answer 19

Fibonacci sequence

Question 20

Who developed the Fibonacci sequence?

Answer 20

Leonardo Fibonacci

Question 21

Fibonacci sequence as a means of _________

Answer 21

Solving practical problems

Question 22

How the Fibonacci sequence formed?

Answer 22

The sequence is formed by starting with 1,1 and adding the two preceding numbers to get the next number.

Question 23

Nature’s numbering system

Answer 23

Fibonacci sequence

Question 24

Where does Fibonacci sequence appear?

Answer 24

In leaf arrangements
Petals of flowers
Bracts of pine cones
Scales of pineapples and
Patterns of seashells

Question 25

The ration of 2 successive Fibonacci numbers.

Answer 25

Golden ratio

Question 26

The golden ratio is approximated by __________.

Answer 26

a+b/b =b/a

Question 27

The set of squares is called the ___________.

Answer 27

Fibonacci rectangles

Question 28

Logic Patterns

Answer 28

Abstract reasoning

Question 29

Involves flexible thinking, creativity, judgment, and logical problem solving.

Answer 29

Abstract reasoning

Question 30

Refers to the ability to analyze information, detect patterns and relationships, and solve problems on a complex, intangible level.

Answer 30

Abstract reasoning

Question 31

Factors to identify the pattern in abstract reasoning

Answer 31

Size Location Color and shades Angles Movement

Question 32

Geomatric Patterns

Answer 32

Tessellation Fractals

Question 33

Created when a shape or combination of shapes are repeated over and over again covering a plane without any gaps or overlaps using transformations.

Answer 33

Tessellation

Question 34

Another word for tessellation

Answer 34

Tiling

Question 35

First used the one shape tessellations

Answer 35

Sumerians at about 4000 B. C. E.

Question 36

Where did the sumerians uses the tessellation?

Answer 36

To build wall decorations in pattern of clay tiles.

Question 37

Some of the most famous tessellations

Answer 37

Moorish wall tiles of Islamic architecture

Question 38

First person to complete a study of tessellation

Answer 38

Johannes Kepler

Question 39

When did Johannes Kepler complete the study of tessellations

Answer 39

After he explored the hexagonal structure of honeycomb and snowflakes.

Question 40

Who began the study of tessellation in mathematics?

Answer 40

Ygraf Fyodorov

Question 41

Ygraf Fyodorov is a ________.

Answer 41

Russian crystallographer

Question 42

Tessellations can be made by

Answer 42

a. Involving a repeated use of one polygon b. Involving repeated use of a unit of shape of two or more different regular polygons. c. Involving triangles or quadrilaterals. d. Of irregular shapes obtained by transformation of other 'more regular' tessellations shapes. e. Involving other irregular shapes.

Question 43

A tessellation made up of congruent regular polygons or polygons whose sides are all the same length.

Answer 43

Regular Tessellation

Question 44

It means that the polygons that you put together are all the same size and shape.

Answer 44

Congruent

Question 45

Three regular polygons tessellate in the Euclidean plane:

Answer 45

Triangles Squares or hexagons

Question 46

Combinations of regular tessellations.

Answer 46

Semi-regular tessellation

Question 47

Properties of semi-regular tessellations:

Answer 47

-it is formed by regular polygons. -the arrangement of polygons at every vertex point is identical.

Question 48

Eight semi-regular tessellations

Answer 48

-3.3.3.4.4 -3.3.4.3.4 -3.4.6.4 -3.6.3.6 -4.8.8 -4.6.12 -3.3.3.3.6 -3.12.12

Question 49

Examples of tessellating quadrilaterals

Answer 49

-tessellating triangles -tessellating rectangles -tessellating a rhombus -tessellating a trapezium and a kite

Question 50

How to produce come irregular shapes to tessellate?

Answer 50

By transforming other shapes which are known to tessellate such as regular polygons.

Question 51

Suitable shapes from which to start making some irregular tessellation

Answer 51

Squares Rectangles Equilateral triangles and Hexagons

Question 52

Methods in making some irregular tessellations

Answer 52

By translating (or sliding) the midpoint of any side of the starting shape making some curved lines. By rotating the midpoint of any side of the starting shape.

Question 53

World famous graphic artist that attributed to the idea of transformation of shapes to create new, irregular, tessellating shapes.

Answer 53

Mauritis Cornelis Escher (1898-1972)

Question 54

A rough or fragmented geometric shape that can be split into two parts, each of which is approximately a reduced size copy of the whole.

Answer 54

Fractals

Question 55

Fractals are often produce by very simple processes—

Answer 55

Reflection, rotation and translation

Question 56

Fractals demonstrate a fourth time of symmetry. They possess ___________.

Answer 56

Self-symmetry

Question 57

A shape is _________ when it looks essentially the same from a distance as it does closer up.

Answer 57

Self-similar

Question 58

Appear the same under magnification.

Answer 58

Self-similar objects

Question 59

Self-similar objects composed of smaller copies of themselves. This characteristic is often referred to as ____________ or _____________.

Answer 59

Scaling symmetry or scale variance

Question 60

Objects like spirals ans nested dolls that are Self-similar around a single point are __________.

Answer 60

Not fractals

Question 61

Exhibit scaling symmetry but only over a limited range of scales.

Answer 61

Natural objects/Fractals in Nature

Question 62

Fractals from mathematical constructions

Answer 62

Coch curve Sierpincki's Triangle

Question 63

Most amazing thing about fractals is the variety of their __________.

Answer 63

Applications

Question 64

Where can we find fractals?

Answer 64

In almost every part of the universe, from bacteria, cultures, to galaxies, and to our bodies.

Question 65

Some of the wide known applications of fractals

Answer 65

In astrophysics Data compression Fractal art Study of music Computer graphics Weather forecasting Human anatomy